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On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups
ISSN: 2149 - 1402
Publisher: author
On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups
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Science General
ARTICLE-FACTOR
1.3
Article Basics Score: 3
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Article Articles Score: 3
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International Category Code (ICC):
ICC-1402
Publisher: Journal Of New Theory Naim Çağman
International Journal Address (IAA):
IAA.ZONE/214977041402
eISSN
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2149 - 1402
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Abstract
Let k>0 an integer. F, τ, N, Nk, and A denote, respectively, the classes of finite, torsion, nilpotent, nilpotent of class at most k, group in which every two generator subgroup is in Nk and abelian groups. The main results of this paper is, firstly, to prove that in the class of finitely generated FN-group, the property FC is closed under finite extension. Secondly, we prove that a finitely generated τN-group in the class ((τNk)τ,∞) ( respectively ((τNk)τ,∞)∗) is a τ-group (respectively τNc for certain integer c=c(k) ) and deduce that a finitely generated FN-group in the class ((FNk)F,∞) (respectively ((FNk)F,∞)∗) is -group (respectively FNc for certain integer c=c(k)). Thirdly we prove that a finitely generated NF-group in the class ((FNk)F,∞) ( respectively ((FNk)F,∞)∗) is F-group (respectively NcF for certain integer c=c(k)). Finally and particularly, we deduce that a finitely generated FN-group in the cl...
